I think I figured it out. A smart mailbox is just a pointer (reference) to the mail messages. It shows all mail in the one folder, but their actual location remains in their original mailboxes.
Mail rules actually MOVE messages from one mailbox to another, which makes even more sense on an IMAP server for synchronizing folders across email clients. A smart folder wouldn't get synchronized. (Unless it somehow did some other trick to synchronize it, I haven't tried that.)
Yep, with rules you can do whatever you need to do (well, nearly). If the sender is something or file does not contain something, hten mark to read and move to folder xyz, if the sender is xyz, then bring to attention immediately etc.